DOI QR코드

DOI QR Code

DISSIPATIVE RANDOM DYNAMICAL SYSTEMS AND LEVINSON CENTER

  • Asmahan A. Yasir (Department of Mathematics, College of Education for Girls, University of Kufa) ;
  • Ihsan J. Kadhim (Department of Mathematics, College of Science, University of Qadisiyah)
  • 투고 : 2022.09.21
  • 심사 : 2023.01.07
  • 발행 : 2023.06.15

초록

In this work, some various types of Dissipativity in random dynamical systems are introduced and studied: point, compact, local, bounded and weak. Moreover, the notion of random Levinson center for compactly dissipative random dynamical systems presented and prove some essential results related with this notion.

키워드

참고문헌

  1. L. Arnold, Random dynamical systems, Dynamical systems, Springer, Berlin, Corrected 2nd printing, 2003. 
  2. L. Arnold and I. Chueshov, Order-Preserving Random Dynamical Systems: Equilibria, attractors, applications, Dyn. Stab. of Sys., 13 (1998), 265-280.  https://doi.org/10.1080/02681119808806264
  3. T. Buhler and D.A. Salamon, Functional analysism Amer, Math. Soc., 2018. 
  4. D.N. Cheban, Nonautonomous Dynamics, Springer Int. Publishing, 2020. 
  5. D. Cheban, On The Structure of The Levinson Center for Monotone Dissipative Nonautonomous Dynamical Systems, Adv. Math. Res. Nova Scie. Pub., 29 (2021), 173-218. 
  6. I. Chueshov, Monotone random systems theory and applications, Springer, 2004. 
  7. A. Gu, S. Zhou and Q. Jin, Random Attractors for Partly Dissipative Stochastic Lattice Dynamical Systems with Multiplicative White Noises, Acta Math. Appl. Sin. English Ser., 31 (2015), 567-576.  https://doi.org/10.1007/s10255-015-0486-0
  8. J. Huang, Random attractor of stochastic partly dissipative systems perturbed by L'evy noise, J. Ineq. Appl., 2012 (2012), 1-13.  https://doi.org/10.1186/1029-242X-2012-1
  9. P. Kloeden and R. Pavani, Dissipative synchronization of nonautonomous and random systems, GAMM-Mitt., 32 (2009), 80-92.  https://doi.org/10.1002/gamm.200910006
  10. C. Kuehn, A. Neamt,u and A. Pein, Random attractors for stochastic partly dissipative systems, Nonlinear Diff. Equ. Appl., NoDEA, 27 (2020), 1-37.  https://doi.org/10.1007/s00030-019-0604-4
  11. S. Kuksin and A. Shirikyan, On dissipative systems perturbed by bounded random kickforces, Ergod. Th. & Dynam. Sys., 22 (2002), 1487-1495. 
  12. A. Mazurov and P. Pakshin, Stochastic dissipativity with risk-sensitive storage function and related control problems, ICIC Expr. Lett., 3 (2009), 53-60. 
  13. T. Rajpurohit and W. Haddad, Dissipativity Theory for Nonlinear Stochastic Dynamical Systems, IEEE Trans. Auto. Control., 62 (2017), 1684-1699.  https://doi.org/10.1109/TAC.2016.2598474
  14. S.M. Ulam and J. Von Neumann, Random ergodic theorems, Bull. Amer. Math. Soc., 51 (1945), 660. 
  15. Y. Wang, Y. Liu and Z. Wang, Random attractors for partly dissipative stochastic lattice dynamical systems, J. Diff. Equ. Appl., 14 (2008), 799-817.  https://doi.org/10.1080/10236190701859542
  16. Z. Wu, M. Cui, X. Xie and P. Shi, Theory of stochastic dissipative systems, IEEE Trans. Autom. Control, 56 (2011), 1650-1655.  https://doi.org/10.1109/TAC.2011.2121370
  17. S. Xiaoying and M. Qiaozhen, Existence of random attractors for weakly dissipative plate equations with memory and additive white noise, Comput. Math. Appl., 73 (2017), 2258-2271.  https://doi.org/10.1016/j.camwa.2017.03.009
  18. L. Yuhong, Z. Brzezniak and Z. Jianzhon, Conceptual Analysis and Random Attractor for Dissipative Random Dynamical Systems, Acta Math. Scienttia, 28 (2008), 253-268. https://doi.org/10.1016/S0252-9602(08)60026-0